An exponentially fitted finite difference method for singular perturbation problems

Abstract

In this paper an exponentially fitted finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer at one end (left or right) point. A fitting factor is introduced in a tridiagonal finite difference scheme and is obtained from the theory of singular perturbations. Thomas algorithm is used to solve the system. The stability of the algorithm is investigated. Several linear and nonlinear problems are solved to demonstrate the applicability of the method. It is observed that the present method approximates the exact solution very well.